document.write( "Question 5550: the length of a rectangle is 2 meters more than its width. The area of the rectangle is 80 square meters. What is the length and width of the rectangle? \n" ); document.write( "
Algebra.Com's Answer #2912 by prince_abubu(198)![]() ![]() ![]() You can put this solution on YOUR website! Alright. We know that the area formula for a rectangle is length * width.\r \n" ); document.write( "\n" ); document.write( "Let's call L the length and W the width.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The first sentence can be translated into L = 2 + W. However, we're going to rewrite that as L = W + 2. Why, you say? Because writing the term with the variable first looks better in writing.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Now, we know that A = L*W. The area is given to us as 80 m^2. But we can't have two unknowns here because that would give us an infinite number of solutions. We'll have to substitute W + 2 for the L so that we're only going to deal with one variable, which is W.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So, \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So now we've got \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "I trust that you know how to factor polynomials and what the factors mean for the equation when you get them. \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Out of w + 10 and w - 8, w - 8 will be the factor that would give us a positive answer to w - 8 = 0. In this case, the answer is 8. We didn't pick the w + 10 because that would've given us a -10 for an answer, which is not a possible value for a length.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Alright. We're almost there. We know now that the width is 8. What about the length? The problem says that the length is 2 meters longer than the width. That would put the length at 10. So the width is 8 and the length is 10. \n" ); document.write( " |